Think of nonprofits as the generic name for any organization that retains income for the organization’s purposes.
A charity is a nonprofit that derives a substantial portion of its support from the public or functions to “support” one or more organizations that are charities and has qualified under Section 501(c)(3) of the Internal Revenue Service Code as tax-exempt.
Private foundations are usually nonprofits that were established and/or sustained with funds from a single source (like family money) or specific sources (like corporate money), rather than being established and/or sustained with funds from the general public and have qualified under Section 501(c)(3) of the Internal Revenue Service Code as tax-exempt.
501(c)(3) is a section of the Internal Revenue Service Code that defines a type of non-profit. “501” refers to tax exemption for certain nonprofits. “(c)(3)” refers specifically to nonprofits that are organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition, or for the prevention of cruelty to children or animals. Being granted 501(c)(3) status allows the nonprofit to avoid paying federal income taxes on most types of revenue, and also allows donors to make tax deductible contributions to the nonprofit.